Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein
homological dimensions for modules over commutative rings. The account includes the …

Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

Let R be a commutative Noetherian ring of Krull dimension d admitting a dualizing complex
D and let 𝔞 be any ideal of R. We prove that is Gorenstein injective for any Gorenstein …

Following our previous work about quasi-projective dimension [11], in this paper, we
introduce quasi-injective dimension as a generalization of injective dimension. We recover …

Let (R, m) be a commutative Noetherian local ring of Krull dimension d, and let C be a
semidualizing R-module. In this paper, it is shown that if R is complete, then C is a dualizing …

R. Sazeedeh showed that top local cohomology modules are Gorenstein injective in a
Gorenstein local ring with at most two dimensions. In this paper, it is proved that the …

Let $ R $ be a commutative noetherian ring. Enochs and Huang [EH] proved that over a
Gorenstein ring of Krull dimension $ d $, every Gorenstein injective module admits a …

Let R be a commutative Noetherian ring and I a proper ideal of R. In this paper, we study
finitely generated R-modules M with only one non-vanishing local cohomology module HI c …

Let (R, m) be a local ring, and let C be a semidualizing R-module. In this paper, we are
concerned with the C-injective and GC-injective dimensions of certain local cohomology …

Let R be a commutative Noetherian ring, 𝔞 be an ideal of R and denote the derived category
of R-modules. We investigate the theory of local homology in conjunction with Gorenstein …